On Minimal Extended Representations of Generalized Power Cones

SIAM Journal on Optimization, Volume 34, Issue 3, Page 3088-3111, September 2024.
Abstract. In this paper, we analyze minimal representations of [math]-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case [math] and [math] are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location.